In digital communications, a bit error rate (BER) is utilized to quantify the ratio of erroneous bits detected relative to the number of transmitted bits. BER can be measured for a given communication system by transmitting a known data pattern and observing the number of errors detected over a duration of testing. In practice, however, many communication systems require BER for a given application to be on the order of 1e−12 or lower. Accordingly, to ensure BER within down to such levels, functional tests often must be performed over extended time periods (e.g., a number of days). For example, given a data rate of approximately 1 giga bits per second (Gbps) would require approximately one day to transmit 100 times 1e12 bits, which would only afford marginally reasonable level of confidence. If the data rate decreases or if the BER requirement reduces, the time requirements to transmit and measure data during functional testing increase accordingly. Such an extensive time periods to perform functional testing are often inappropriate in many circumstances associated with production and testing of circuit components.
Because of the impractical time requirements associated with performing measurements in bit-by-bit simulations, alternative techniques have been developed to estimate BER. Many of these alternative techniques employ statistical approaches to estimate BER, such as methods using probability distribution functions (PDFs). For example, the overall channel including the transmitter and receiver are modeled linearly, such as being approximated by a linear finite impulse response (FIR) filter. The model can be analyzed to compute filter taps corresponding to intersymbol interference. A similar PDF for crosstalk noise can also be computed. Because of the constraints associated with such statistical approaches, other non-idealities associated with the communication system typically remain unaccounted for. This tends to result in inaccuracies associated with the estimated BER.